Problem: Luis is 30 years younger than William. For the last two years, William and Luis have been going to the same school. Fifteen years ago, William was 4 times older than Luis. How old is William now?
We can use the given information to write down two equations that describe the ages of William and Luis. Let William's current age be $w$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $w = l + 30$ Fifteen years ago, William was $w - 15$ years old, and Luis was $l - 15$ years old. The information in the second sentence can be expressed in the following equation: $w - 15 = 4(l - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to solve our first equation for $l$ and substitute it into our second equation. Solving our first equation for $l$ , we get: $l = w - 30$ . Substituting this into our second equation, we get the equation: $w - 15 = 4($ $(w - 30)$ $ -$ $ 15)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $w - 15 = 4w - 180$ Solving for $w$ , we get: $3 w = 165$ $w = 55$.